Harold has 4 cups of trail mix. He wants to give 1/3 cup trail mix to each camper in his group.There are 8 campers in his group. Does he have enough trail mix for all the campers?Explain.

y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.

Answer:

A

Step-by-step explanation:

Final answer:

The quadratic function equivalent to the polynomial 2 + 7c – 4c2 – 3c + 4 when simplified and written in standard form is – 4c2 + 4c + 6.

Explanation:

When you simplify and write the polynomial 2 + 7c – 4c2 – 3c + 4 in standard form, the quadratic function equivalent is – 4c2 + 4c + 6. First, combine like terms by adding the constants and the terms with c. This gives you – 4c2 + (7c – 3c) + (2 + 4), which simplifies to – 4c2 + 4c + 6.

The standard form of a quadratic equation is ax2 + bx + c = 0. In the case of the simplified polynomial, a = -4, b = 4, and c = 6. If needed, you can use the quadratic formula to find the roots of this quadratic equation by substituting these values into the formula.

Answer:

3x^2−13x+4

Step-by-step explanation:

(x−4)(3x−1)

=(x+−4)(3x+−1)

=(x)(3x)+(x)(−1)+(−4)(3x)+(−4)(−1)

=3x^2−x−12x+4

=3x^2−13x+4

Answer:

Option A. 3x² - 13x + 4 is the answer.

Step-by-step explanation:

A conference room is in the shape of a rectangle. Its floor has a length of (x - 4) and width of (3x - 1) meters.

The expression that represents the area of the room is (x - 4)(3x -1) meter²

We further simplify this expression representing the area of the conference room.

(x - 4)(3x -1) = x(3x -1) - 4(3x -1) [Distributive law]

= 3x² - x - 12x + 4

= 3x² - 13x + 4

Option A. 3x² - 13x + 4 is the simplified form of the given expression.

Answer:

[tex]\large\boxed{B.\ x=\dfrac{5+\sqrt{21}}{2},\ C.\ x=\dfrac{5-\sqrt{21}}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\================================\\\\\text{We have}:\\\\x^2+1=5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\x^2-5x+1=0\\\\a=1,\ b=-5,\ c=1\\\\b^2-4ac=(-5)^2-4(1)(1)=25-4=21\\\\x=\dfrac{-(-5)\pm\sqrt{21}}{2(1)}=\dfrac{5\pm\sqrt{21}}{2}[/tex]

Answer:

b and c Apex answers

[tex]4x^{2} -4x - 1 = 0[/tex]

To solve for the zeros you can use the quadratic formula:

[tex]\frac{-b plus/minus\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 4

b = -4

c = -1

[tex]\frac{-(-4) plus/minus\sqrt{(-4)^{2}-4(4)(-1) } }{2(4)}[/tex]

[tex]\frac{4 plus/minus\sqrt{16+16 } }{8}[/tex]

[tex]\frac{4plus/minus\sqrt{32} }{8}[/tex]

[tex]\frac{4plus/minus4\sqrt{2 } }{8}[/tex]

[tex]\frac{1 plus/minus\sqrt{2} }{2}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

The quadratic equation 4x^2 - 4x - 1 = 0 can be solved by using the quadratic formula -b ± √b² - 4ac / 2a. After substituting the coefficients into the formula, we get 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4. These roots are the solution to the equation.

The subject of the question is the solution of a quadratic equation which can be found using the quadratic formula. For the given equation 4x^2 - 4x - 1 = 0, the values of a, b, and c as per the general quadratic equation (ax^2 + bx + c = 0) are a = 4, b = -4 and c = -1. The quadratic formula to solve for x is -b ± √b² - 4ac / 2a.

Substituting the given values in to the formula we get the solution for x: 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4, which can further be solved to get the two roots of the quadratic equation.

https://brainly.com/question/30398551

#SPJ3

Answer:

The value of x is 2.5 to the nearest tenth

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problem

∵ x is opposite to the angle of measure 23°

∵ 6 is adjacent to the angle of measure 23°

∴ tan(23°) = x/6 ⇒ × 6 to both sides

∴ x = 6 × tan(23°) = 2.5

* The value of x is 2.5 to the nearest tenth

Answer: [tex]x=2.5[/tex]

Step-by-step explanation:

You need to remember the identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

You can identify in the figure that for the angle 67°:

[tex]\alpha=67\°\\opposite=6\\adjacent=x[/tex]

Then you need to substitute these values into  [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for "x":

[tex]tan(67\°)=\frac{6}{x}\\\\xtan(67\°)=6\\\\x=\frac{6}{tan(67\°)}\\\\x=2.5[/tex]

Answer:

1. x = 49.10 - 5 divided by 2.10

2. 21 miles

Answer:

X=49.10

21 miles

Step-by-step explanation:

First, you need to divide 2.10 and the $5 . which will give you 4.2.

this has nothing to do with the problem lol.

I would keep on mulitiplying if i were you.

And, once you hit 21 miles, you will get $44.10 and the $5 which will equal 49.10 :).

Answer:

first number is 2, second number is 2

Step-by-step explanation:

If the first number is 'a' and second number is 'b'. We can use simultaneous equations

9a + 4b = 26

3a + 4b = 14

therefore by taking the second equation from the first

6a = 12

a = 2 (first number)

as a = 2

(3 x 2) + 4b = 14

6 + 4b = 14

4b = 8

b = 2 (second number)

By setting up a system of equations, we find that the two mystery numbers are both 2. This conclusion is reached by first eliminating the variable representing the second number and then solving for the first number, which turns out to be 2. Subsequently, the value of the second number is also determined to be 2.

We can solve for the two mystery numbers by setting up a system of linear equations based on the information given:

9 times the first number plus 4 times the second number equals 26.

3 times the first number plus 4 times the second number equals 14.

Let's designate the first number as x and the second number as y. Then, we can express the problem using equations:

9x + 4y = 26 (1)

3x + 4y = 14 (2)

Next, we'll solve this system of equations. We can start by subtracting equation (2) from equation (1), which will remove y from the equations, as the coefficients before y are the same:

(9x + 4y) - (3x + 4y) = 26 - 14

6x = 12

After simplifying the equation, we find that:

x = 12 / 6

x = 2

Now that we have the value for x, we can substitute it back into either (1) or (2) to find y:

9(2) + 4y = 26

18 + 4y = 26

4y = 26 - 18

4y = 8

y = 8 / 4

y = 2

Therefore, the first number is 2 and the second number is also 2.

Answer:

sin(150°) = 1/2

Step-by-step explanation:

* Lets study how we can solve this problem

- At first the measure of the angle is 150°

- Ask your self in which quadrant can you find this measure

* To know the answer lets revise the four quadrants

# First quadrant the measure of all angles is between 0° and 90°

  the measure of any angle is α

∴ All the angles are acute

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between 90° and 180°

  the measure of any angle is 180° - α

∴ All the angles are obtuse

∴ The value of sin(180° - α) only is positive ⇒ sin(180° - α) = sinα

# Third quadrant the measure of all angles is between 180° and 270°

  the measure of any angle is 180° + α

∴ All the angles are reflex

∴ The value of tan(180° + α) only is positive ⇒ tan(180° + α) = tanα

# Fourth quadrant the measure of all angles is between 270° and 360°

  the measure of any angle is 360° - α

∴ All the angles are reflex

∴ The value of cos(360° - α) only is positive ⇒ cos(360° - α) = cosα

* Now lets check the angle of measure 150

- It is an obtuse angle

∴ It is in the second quadrant

∴ the value of sin(150) is positive

∴ sin(150°) = sinα

∵ 180 - α = 150 ⇒ isolate α

∵ α = 180° - 150° = 30°

∴ sin(150°) = sin(30°)

∵ sin(30°) = 1/2

∴ sin(150°) = 1/2

ANSWER

[tex]\sin(150 \degree) = \frac{1}{2} [/tex]

EXPLANATION

The principal angle for 150° is 30°.

The terminal side of 150° is in the second quadrant.

In this quadrant the sine ratio is positive.

This implies that;

[tex] \sin(150 \degree)= \sin(30 \degree) [/tex]

On the unit circle,

[tex] \sin(30 \degree) = \frac{ 1 }{2} [/tex]

Therefore

[tex]\sin(150 \degree)= \sin(30 \degree) = \frac{1 }{2} [/tex]

Answer:

[tex]k=26/3[/tex]

Step-by-step explanation:

we have

[tex]g(x)=3k-5x[/tex]

we know that

If the graph of g(x) passes through the point (3,11)

then

the ordered pair (3,11) must satisfy the equation g(x)

Substitute

[tex]x=3,g(3)=11[/tex]

[tex]11=3k-5(3)[/tex]

[tex]11=3k-15[/tex]

[tex]3k=11+15[/tex]

[tex]3k=26[/tex]

[tex]3k=26[/tex]

[tex]k=26/3[/tex]

Answer:

it would take her 7 days

Step-by-step explanation:

Answer:

7 days

Step-by-step explanation:

90-118=(-28)

28° to go.

12°/3 days = 4° per day

28/4=7. 7 days

Answer:

Chicago's temperature < Phoenix's temperature

Step-by-step explanation:

Because -1°F is less than 40°F.

Answer:

Area = 575m²  Perimeter = 94

Step-by-step explanation:

Trust me I'm right

Answer:

Area of the Figure: 575 m

Perimeter of the Figure: 94 m

Step-by-step explanation:

That shape can easily be divided into a right triangle and a rectangle.

•••To solve the area for the rectangle:

base x height

17 * 25 = 425 m

•••To solve the area for the right triangle:

1/2 x base x height

1/2 x 15 x 20 = 150 m

•••Perimeter of the figure:

Add all the sides.

17 + 17 + 25 + 15 + 20 = 94 m

The answer is:

The population in 2015 will be 1,412,415.

Since from the statement we know that the population is increasing, we know that we are working with an exponential growth problem.

We can calculate the exponential growth using the following equation:

[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]

Where,

P, is the population after t (years, months, days or hours)

Start Population, is the starting population.

Growth percent, is the percent of growth

t, is the time elapsed (years, months, days or hours)

So, we are given the following information:

[tex]StartPopulation=478434\\\\GrowthPercent=7(percent)=\frac{7(percent)}{100}=0.07\\\\TimeElapsed=2015-1999=16years[/tex]

Now, substituting and calculating, we have:

[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]

[tex]Population(t)=478434(1+0.07)^{16}=141241.5=1412415[/tex]

Hence, the population in 2015 will be 1,412,415.

Have a nice day!

Answer:

The amount of medicine in the patient's blood after 20 minutes is 2.6906 milligrams

Step-by-step explanation:

The amount of medicine in the patient's blood after 20 minutes will given by;

f(20)

since we are informed that the amount f(t) of a certain medicine in a patient's bloodstream t minutes after being taken is given by f(t);

We simply substitute t = 20 in the function f(t);

[tex]f(20)=\frac{60(20)}{20^{2}+46 }=2.6906[/tex]

Answer:

Step-by-step explanation:

Since the formula is given, we only need to substitute 20 for t to find the answer.

60t/t sq. + 46 we substitute 20 for x:

60(20)/ 20x20 +46

1200/446 which equals

2.6905 milligrams

[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x\stackrel{\stackrel{b}{\downarrow }}{-3}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad \cfrac{7}{5};-3[/tex]

The formula y=mx+b which this equation is in shows the slope as m and y-intercept as b. In this situation where m is the fraction 7 over 5 and b is -3. So the slope is 7/5 and the y-intercept is -3

Answer:

a.

                         R-------8/38--------RR

R------9/39--------B-------13/38-------RB

                          G------17/38--------RG

                          R-------9/38--------BR

B--------13/39------B-------12/38-------BB

                           G-------17/38-------BG

                             R-----9/38--------GR

G---------17/39-------B------13/38-------GB

                              G------16/38-------GG

b).

RB=9/39 × 13/38=3/38

BR= 13/39 × 9/38 =3/38

BG= 13/39 × 17/38=17/114

GB= 17/39 × 13/38=17/114

=3/38 +3/38+17/114+ 17/114 =26/57

ANSWER

[tex](g \circ \: f)(0) = - 216[/tex]

EXPLANATION

The functions are:

[tex]f(x) = 2x - 6[/tex]

[tex]g(x) = {x}^{3} [/tex]

[tex](g \circ \: f)(x) =g(f(x))[/tex]

[tex](g \circ \: f)(x) =g(2x - 6)[/tex]

We substitute f(x) into g(x) to obtain:

[tex](g \circ \: f)(x) =(2x - 6)^{3} [/tex]

We now substitute x=0 to obtain;

[tex](g \circ \: f)(0) =(2(0) - 6)^{3} [/tex]

[tex](g \circ \: f)(0) =(- 6)^{3} [/tex]

This simplifies to:

[tex](g \circ \: f)(0) = - 216[/tex]

Answer:

B and D

Step-by-step explanation:

if they had letters it would be

A     B

C     D

options B and D are similar

Answer:

II and IV

Step-by-step explanation:

We are given that four figures

We have to find two similar figures.

Similar figures: Two triangle are called similar when the ratio of corresponding sides are equal and corresponding angles are equal.

In Second and fourth figure

Each angle of second figure  is equal to its  corresponding angle of fourth figure.

Ratio of corresponding sides

[tex]\frac{6}{12}=\frac{1}{2}[/tex]

[tex]\frac{2.5}{5}=\frac{1}{2}[/tex]

[tex]\frac{6.5}{13}=\frac{1}{2}[/tex]

[tex]\frac{6}{12}=\frac{2.5}{5}=\frac{6.5}{13}[/tex]

Hence, second and fourth figure are similar to each other.

Answer:

a*b = 8

Step-by-step explanation:

a-b =2

Let b= 2

a-2 =2

Add 2 to each side

a-2+2 =2+2

a =4

We want to find a*b

4*2 = 8

a*b = 8

First substitute 2 in for b to get a - (2) = 2.

Now isolate a by adding 2 to both sides to get a = 4.

Since a = 4, substitute 4 in for a and 2 in for b to get 4 × 2.

Multiplying, 4 × 2 gives us a product of 8.

So the value of a × b is 8.

Answer:

It will reach 0 degrees celcius at 5:20AM i believ

Step-by-step explanation:

If you divide 8 by 1.5 you bet 5 and 1/3

5 1/3 turns to 5:20 AM

Answer:

86 4/7, C.

Step-by-step explanation:

14x6= 84

       +

6 x 3/7 = 2 4/7

86 4/7

Answer:

multiply 14 over 7 to get the number as one fraction. after adding three to that product, you get 101/7. Multiply that by 6/1 to get 606/7, then divide 606 by 7 to get 86 4/7 hours every 6 months.

Step-by-step explanation:

Answer:

2. The reasonable domain is restricted to positive real numbers.

Step-by-step explanation:

The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.

___

I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.

__

x might be restricted to integers if you're only measuring the remaining amount once a year.

The maximum value of 1500 applies to the *range* of the function, not its domain.

The minimum value of 1500 has nothing to do with anything.

Answer:

B) the reasonable domain is restricted to positive real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5x + 10 = 15y

(-5(x-2))/15

(-x+2)/3 = y

5x - 10((-x+2)/3)

5x - ((-10x + 20)/3)=-40

5x + (10x-20)/3

15x + 10x - 20 = -120

25x = -100

x = -4

5x + 15y = 10

-20 + 15y = 10

30 = 15y

y = 2

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x+15y=10\\5x-10y=-40&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x+15y=10\\-5x+10y=40\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad25y=50\qquad\text{divide both sides by 25}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the first equation:}\\\\5x+15(2)=10\\5x+30=10\qquad\text{subtract 30 from both sides}\\5x=-20\qquad\text{divide both sides by 5}\\\boxed{x=-4}[/tex]

Answer:

He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex]

Step-by-step explanation:

We need to remember that:

[tex]\sqrt[n]{x^n}=x[/tex]

The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

The Power of a power a property states that:

[tex](a^m)^n=a^{(mn)}[/tex]

Let's check the procedure made by Jamal to simplify the expression [tex]\sqrt{75x^5y^8 }[/tex] where [tex]x\geq0[/tex] and [tex]y\geq0[/tex]:

[tex]=\sqrt{25*3*x^4*x*y^8}[/tex] (This is correct)

[tex]5x^2y^2\sqrt{3x}[/tex] (Jamal made a mistake)

The correct procedure is:

[tex]=\sqrt{25*3*x^4*x*y^8}[/tex]

[tex]=5x^2y^4\sqrt{3x}[/tex]

Because:

[tex]\sqrt{y^8}=\sqrt{(y^4)^2}=y^4[/tex]

Therefore: He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex],

Answer:

He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

Step-by-step explanation:

its A on Ed

We have

[tex]a^b\cdot a^c=a^{b+c}[/tex]

[tex]a^b\div a^c=a^{b-c}[/tex]

So, in your case, we have

[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]

Answer:

Option D. 1/64

Step-by-step explanation:

We have to simplify the following expression

[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]

= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]

= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]

= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]

= [tex]4^{-\frac{9}{3}}[/tex]

= [tex]4^{-3}[/tex]

= [tex]\frac{1}{4^{3} }[/tex]  [[tex]a^{-1}=\frac{1}{a}[/tex]]

= [tex]\frac{1}{64}[/tex]

Option D. 1/64 is the answer.

Answer:

37, 39

Step-by-step explanation:

n + 1/3 (n + 2) = 50

Multiply both sides by 3 to cancel out the 1/3:

3n + (n + 2) = 150

Simplify:

4n + 2 = 150

4n = 148

n = 37

n + 2 = 39

Answer:

37 and 39.

Step-by-step explanation:

Let the two odd numbers are x and ( x + 2 ) Then by statement " Sum of the first number and one third of second number is equal to 50."

So equation will be

x + [tex]\frac{1}{3}[/tex] (x+2) = 50

We multiply the equation by 3

3x + ( x+2 ) = 150

3x + x + 2 = 150

4x + 2 = 150

4x = 150 - 2 = 148

x = 37

So numbers are 37 and 39.

Answer:

[tex]\large\boxed{A=9x^2-6xy+y^2}[/tex]

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have s = 3x - y. substitute:

[tex]A=(3x-y)^2[/tex]           use (a - b)² = a² - 2ab + b²

[tex]A=(3x)^2-(2)(3x)(y)+y^2=9x^2-6xy+y^2[/tex]

Answer:

1017.36 square inches

Step-by-step explanation:

The globe is in the shape of a sphere. As we given the diameter of the globe

d = 18 inches

We have to find the radius of globe first

[tex]Radius=r=\frac{d}{2}\\r=\frac{18}{2}\\r=9\ inches[/tex]

The formula for finding the surface area is:

[tex]Surface\ Area=4\pi r^{2}\\Putting\ the\ values\ of \pi \ and\ r\\Area=4*3.14*(9)^{2} \\=4*3.14*81\\=1017.36\ square\ inches[/tex]

Hence, the surface area is 1017.36 square inches ..

Answer:

10r⁵ + 2r⁴ + 5r²

Step-by-step explanation:

A = 90r⁶ + 28r⁵ + 2r⁴ + 45r³ + 5r²

Factor our r²:

A = r² (90r⁴ + 28r³ + 2r² + 45r + 5)

Factor 2r² from the first three terms and 5 from the last two:

A = r² (2r² (45r² + 14r + 1) + 5 (9r + 1))

Factor the trinomial:

A = r² (2r² (5r + 1)(9r + 1) + 5 (9r + 1))

Factor out 9r+1:

A = r² (2r² (5r + 1) + 5) (9r + 1)

Distribute the 2r²:

A = r² (10r³ + 2r² + 5) (9r + 1)

Distribute the r²:

A = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

The area is width times length, and the width is 9r + 1.

WL = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

(9r + 1) L = (10r⁵ + 2r⁴ + 5r²) (9r + 1)

L = 10r⁵ + 2r⁴ + 5r²

The length of the pool is 10r⁵ + 2r⁴ + 5r².